I just bought the phone myself in early December. I have the same problem as you do too. When I call my mom (she has telus) the first time, it just hangs up or rings once and hangs up again. I have to call twice in order to make the call. At first, I just thought it didn't go through but I had to do the same thing every time I called my mom.
I don't have the problem where my phone turns off by itself though..
I'm so glad that I'm not the only who has this problem. I'm thinking of bringing it back to Rogers and getting them to look at it.